Notice that this preface was written in a early form of kana form right to left. Namely, there's many old hentaigana originated from cursive chinese characters. For clarity, The corresponding modern hiragana will be indicated just behind the old one. Additionally, in the 12th century, there's not explicit way to mark voicing, so voicing diacritic will be dropped completely in the following transcript.

つ(の)哥(歌)(は)　み(か)とのおほ(む)(は)(し)
め(な)(り)　おほさ〳〵(き)のみ(か)との
(な)(に)(は)つ(に)てみこときこ(ヤ行え)
けると(き)　とう宮をた(か)ひ(に)
ゆつ(り)て　くらゐ(に)つ(き)たま(は)
て　みとせ(に)な(り)(に)(け)(れ)(は)　王

(に)と言ふ人のいふ(か)(り)(お)(も)ひ
(て)　よみてたてまつ(り)ける哥(歌)
(な)(り)　この(は)(な)(は)ん(む)めの花をい
(ふ)なる(へ)(し)　あ(さ)(か)や万(ま)のこと
(は)〳〵　うねめの(た)はふれよ(り)
よみて　か(つ)らき(の)お(ほ)(き)みを

"〱" is just a old iteration mark denoting the repetition of the previous kana.

The Kanji "哥" is the simplified(or wrong) form of "歌".

Transliterating hentaigana into hiragana:

つの歌は　みかとのおほむはし
めなり　おほささきのみかとの
なにはつにてみこときこえ
けるとき　とう宮をたかひに
ゆつりて　くらゐにつきたまは
て　みとせになりにけれは　王

にと言ふ人のいふかりおもひ
て　よみてたてまつりける歌
なり　このはなはむめの花をい
ふなるへし　あさかやまのこと
はは　うねめのたはふれより
よみて　かつらきのおほきみを

Final transliteration with kanji: